Academic Paper Writing Service http://StudyHub.vip/Anonymous-Communication-For-Encouraging 👈

1. Abstract— We propose an application of DC-net called Layered
DC-net for encouraging the reporting of wrongdoing in social
groups. A social group is a set of individuals, structured into lay-
ered subgroups. Individuals are divided into subgroups called
lower groups. One of the individuals in each lower group is a rep-
resentative who has authority and responsibility for the lower
group. The set of all representatives from all lower groups is
called the upper group. In social groups, wrongdoing (e.g., bully-
ing in schools) occasionally occurs. If individuals in a lower group
discover wrongdoing, they should report it to their representative.
Meanwhile, all representatives are responsible for settling
wrongdoing. However, once individuals reporting such wrong-
doing and their representative are identified, the payoffs for both
are smaller than those for individuals who do not report it. We
focus on reporting bullying in a school as an example of reporting
wrongdoing in social groups. By using game theory, we formulate
a game among bystanders of bullying in a lower group and an-
other game among teachers in the upper group. We evaluate the
games with and without the Layered DC-net. The results show
that the Layered DC-net implements the Nash equilibria that
encourage the reporting of wrongdoing in both lower and upper
groups and settles wrongdoing in the social group.
I. INTRODUCTION
There exist several social groups, each of which has common
goals, in society. In this paper, a social group is a set of indi-
viduals, structured into layered subgroups. Individuals are
divided into subgroups called lower groups. One of the indi-
viduals in each lower group is a representative who has au-
thority and responsibility for the lower group. The set of all
representatives from all lower groups is called the upper group.
Schools and companies are examples of such social groups. A
school has educational goals and is structured into classes and
the staff. Each class corresponds to a lower group composed of
students and their teacher. The staff correspond to the upper
group composed of teachers. A company has commercial goals
and is structured into departments and the board. Each de-
partment corresponds to a lower group composed of employees
and their managing executive. The board corresponds to the
upper group composed of executives.
By using game theory, behaviors of individuals can be
formulated by payoffs [1]. When a social group achieves its
goal, the payoffs for individuals and representatives in the
social group are large. For instance, as the business of a com-
pany expands, the incomes of employees and executives will
become higher. Meanwhile, when wrongdoing preventing the
achievement of a goal occurs in a social group, payoffs for
individuals and representatives in the social group are small.
For instance, bullying in a school or misconduct in a company
is wrongdoing. If wrongdoing is discovered in a social group,
its external reputation will suffer. Consequently, the payoffs for
all individuals and representatives in the social group will also
be small.
Thus, if individuals in a lower group discover wrongdoing,
they should report it to the others in the lower group and their
representative in order to settling it. For instance, if students in
a class at school discover bullying, they should report it to their
classmates and their teacher. In another instance, if employees
discover misconduct in a department at their company, they
should report it to their colleagues in the department as well as
their executive in the interests of the company and society at
large. The representative (e.g., teacher or executive) who re-
ceived such reports is responsible for settling wrongdoing. In
the same way, if a representative receives reports of wrongdo-
ing in her lower group, she should report it to the other repre-
sentatives to settle it. For instance, a teacher who received
reports of bullying in her class should report it to the other
teachers in order to take school-wide anti-bullying measures.
All of the representatives (e.g., teachers or executives) in the
social group are also responsible for settling wrongdoing.
However, once individuals reporting wrongdoing are identi-
fied, their payoffs may be smaller than those for individuals
who do not report it when wrongdoing is not settled and it
continues. In the case of bullying at school, once students re-
porting the bullying are identified, they may then also become
victims when bullying is not settled and continues as a conse-
quence. In order to encourage the reporting of wrongdoing, it is
necessary to prevent individuals who report it and their repre-
sentative from being identified. If the anonymity of the indi-
viduals reporting wrongdoing and that of their representative
are protected through the use of anonymous communication
techniques, they can retain a large payoff.
In this paper, we propose an application of DC-net called
Layered DC-net for encouraging the reporting of wrongdoing
in social groups, structured into layered subgroups (i.e., lower
groups and an upper group). When individuals in each lower
group report wrongdoing, the Layered DC-net can (1) broad-
cast the number of reports within each lower group while
maintaining the anonymity of the individuals reporting it and
(2) broadcast the existence of individuals reporting it within the
Anonymous Communication for Encouraging
the Reporting of Wrongdoing in Social Groups
Kohei Sugiyama*, Masaki Fukushima* and Teruyuki Hasegawa*
* KDDI R&D Laboratories, Inc.
2-1-15 Ohara, Fujimino-shi, Saitama, 356-8502 Japan
E-mail: {ko-sugiyama, fukusima, teru}@kddilabs.jp
978-1-4244-8915-2/10/$26.00 ©2010 IEEE 37

2. upper group while maintaining the anonymity of the individu-
als reporting it and that of their representative.
We also evaluate the effectiveness of the Layered DC-net.
We focus on reporting bullying at a school as an example of
reporting wrongdoing in social groups. By using game theory,
we formulate a game among students in a lower group and
another game among teachers in the upper group. We evaluate
the games with and without the Layered DC-net. The results
show that the Layered DC-net implements the Nash equilibria
that encourage the reporting wrongdoing in both lower and
upper groups and settles wrongdoing in the social group.
The organization of this paper is as follows. First, related
work is summarized in Section II. In Section III, an application
of DC-net is proposed. In Section IV, we focus on reporting
bullying in a school as an example of reporting wrongdoing in
social groups. By using game theory, we formulate a game
among students and another game among teachers. In Section
V, we evaluate the games with and without the Layered DC-net.
Finally, Section VI concludes this paper and discusses future
works.
II. RELATED WORK
Previously, several anonymous communication techniques
have been proposed [2,3]. The author of [2] proposes an
anonymous communication protocol called DC-net (Dining
Cryptographers NETwork), where an individual broadcast a
message among individuals. DC-net ensures infor-
mation-theoretic sender and receiver anonymity. However,
DC-net has a scalability drawback in terms of the number of
individuals. In addition, DC-net is not designed for a group
structured into layered subgroups, in other words, it assumes
only a single group where all individuals compose one flat
group. The authors of [3] propose a scalable anonymous
communication system based on DC-net called Herbivore.
Herbivore improves scalability in terms of the number of indi-
viduals by dividing a group into subgroups. However, since
Herbivore realizes anonymity within each subgroup corre-
sponding to a lower group, it cannot prevent each subgroup (i.e.,
each representative) from being identified.
Meanwhile, the effectiveness of anonymous communication
protocols has been investigated by using game theory [4]. The
authors of [4] analyze the effect of the behavior of individuals
on the anonymity of DC-net. However, effects of anonymous
communication protocols on behaviors of individuals are not
investigated. In this paper, we investigate the effect of the
Layered DC-net on behavior of individuals and representatives
in social groups.
III. PROPOSED APPLICATION OF ANONYMOUS
COMMUNICATION PROTOCOL
Assuming that L lower groups exist in a social group, when
individuals in each lower group report wrongdoing, the Lay-
ered DC-net can (1) broadcast the number of reports within
each lower group while maintaining the anonymity of the in-
dividuals reporting it and (2) broadcast the existence of indi-
viduals reporting it within the upper group while maintaining
the anonymity of the individuals reporting it and that of their
representative.
We design the Layered DC-net based on DC-net [2]. DC-net
is a function to compute confidential inputs from individuals 1,
…, n in a group formulated as follows:
where is a parameter, is the
input from individual , and ∑ is the
output to all individuals. However, since DC-net assumes a
group without layered structure where all individuals compose
one flat group, individual in a subgroup composing a group
cannot distinguish the output ∑ from the output
∑ .
The assumptions in the Layered DC-net are as follows: (1)
individuals operate with a discrete interval called a phase and
(2) a point-to-point communication channel exists between
every pair of individuals in a lower group. The network model
assumed in the Layered DC-net is shown in Fig. 1.
Figure 1: Network model assumed in the Layered DC-net
In the Layered DC-net, the following operations are exe-
cuted.
 Phase 1
The individuals { | |} of each subgroup
in the lower groups execute DC-net.
� 1 � |� |
∑
where ∑ is output to individuals in each subgroup .
 Phase 2
In the upper group (i.e., subgroup 4), individuals of the upper
group (i.e., representatives of lower groups) take the output of
phase 1 as inputs and execute DC-net.
� ( � � � ) � (∑ )
where f(x) is defined as:
� {
and is output to individuals in the upper groups.
]
Upper group
Lower groups
Individual
Subgroup 1
Subgroup 2
Subgroup 3
Subgroup 4
Representatives
38

3. IV. FORMULATION OF WRONGDOING IN SOCIAL GROUPS USING
GAME THEORY
A. Reporting Bullying in a School
In this paper, we focus on reporting bullying in a school as an
example of reporting wrongdoing in social groups. In this
example, a lower group is a class composed of a teacher and
students and the upper group is the staff composed of teachers.
Note that the model in this paper formulates the behavior of
bystanders of bullying in a class, rather than that of perpetrators
and victims of bullying in the class.
When bullying exists in a class, it cannot be settled unless
bystanders report it. If the bullying is not settled, the bystanders
feel guilty. Thus, their payoffs are small. On the other hand, if
the bullying is settled, their payoffs are large. However, if
bystanders report the bullying, they might be identified by the
perpetrators of the bullying and then become victims of the
bullying as retaliation by the perpetrators, which makes their
payoffs quite small.
Moreover, when bullying exists in a class, it cannot be settled
unless teachers agree to take school-wide anti-bullying
measures. If the bullying is not settled, the reputation of the
teachers involved is adversely affected. Thus, their payoffs are
small. On the other hand, if the bullying is settled, their payoffs
are large. However, if a teacher with bullying in her class agrees
to school-wide anti-bullying measures, she might be identified
and her reputation within the school may be even more ad-
versely affected, which makes her payoff quite small. In the
case of reporting bullying, individuals should report bullying to
maintain the external reputation of their school. However, if
they are identified, their payoffs might be quite small.
In this paper, we formulate bullying in a school using game
theory. First, the behavior of bystanders in a class is formulated
as a game among the bystanders in a lower group to investigate
whether the bystanders report the bullying to their teacher.
Second, the behavior of teachers in the staff is formulated as a
game among the teachers in an upper group to investigate
whether all the teachers collaboratively take school-wide an-
ti-bullying measures. We then formulate additional games with
the Layered DC-net.
B. Game among Bystanders
In this section, we formulate a game among bystanders based
on [5]. In this game, it is assumed that if the number of by-
standers reporting bullying is more than a threshold
out of bystanders, their teacher recognizes the bullying. If
school-wide anti-bullying measures are taken by all the teach-
ers, it is then regarded as settled.
We first formulate a game without the Layered DC-net.
Assuming that each bystander determines her behavior whether
she reports bullying or not without interaction with the other
bystanders and she knows that all bystanders have a common
payoff function, her behavior is formulated as a
non-cooperative complete-information game denoted by
. is a finite set of bystanders,
each of which is indexed by . = is a finite set
of strategies available to bystanders called their strategy
space, where is the
strategy space of bystander . is a finite set of
payoff functions for bystanders. When all bystanders’
strategies are , the payoff for by-
stander is defined as:
{
where | | | is the number of
bystanders playing strategy R, is the base line of a bystand-
er’s payoff when there is no bullying in a class, is the cost
when bullying continues and is the cost for reporting bullying
when bullying continues (i.e., the risk of retaliation).
The payoff for bystander is shown in Tab. 1. By-
stander ’s strategy determines a row, and the total number
of bystanders playing strategy R except bystanders
determines a column, where .
Table 1: Payoff for bystanders
… …
R … …
S … …
We next formulate a game with the Layered DC-net as an-
other non-cooperative complete-information game denoted by
. In this case, we assume that the cost for re-
porting bullying becomes ⁄ for the information-theoretic
anonymity of the Layered DC-net based on DC-net [2] and
payoff for bystander is defined as:
{
C. Game among Teachers
In this section, we formulate a game among teachers where a
teacher with bullying in her class knows that bullying is taking
place, however, the other teachers are not aware of it. In this
game, all teachers vote on whether or not they should take
school-wide anti-bullying measures. If the number of teachers
agreeing exceeds a certain threshold, measures are taken to
uncover and settle the bullying. To evaluate the qualitative
characteristics of this game simply, in this paper we analyze a
game between two teachers as a fundamental model, where the
threshold is 1.
We first formulate a game without the Layered DC-net. As-
suming that what each teacher knows about the other teacher is
only the probability that there is bullying in the other teacher’s
class, her behavior is formulated as a non-cooperative incom-
plete-information game (a.k.a., a Bayesian game [1]) denoted
by . is a set of teachers, each of
which is indexed by . is a set of actions
available to these teachers called their action space, where
is the action space of teacher .
is a set of possible types of teachers called their
type space, where {B: with bullying in her class, C:
without bullying in her class} is the type space of teacher .
39

4. is the probability of a type and
( ) is the payoff function for these
teachers, where . The payoff for teacher ,
, is defined as:
{
,
where is the number of teachers playing action F, is
the base line of a teacher’s payoff when there is no bullying in
her class, is the cost caused by the degradation of the external
reputation of the school when bullying continues, is the cost
for taking school-wide anti-bullying measures, is the cost
caused by the degradation of the reputation of the teacher with
bullying in her class when the bullying is discovered, is the
cost caused by that teacher when she disagrees to take an-
ti-bullying measures when bullying is discovered in her class.
For evaluating this Bayesian game , we transform this
game to a complete-information game .
is the strategy space of all teachers where , is the
strategy space of teacher , which consists of a set of all func-
tions from to . This means each teacher determines
whether she agrees or disagrees after becoming aware whether
there is bullying in her class or not.
( ) is the set of payoff functions for
these teachers, where is payoff for teacher when the
strategies of all teachers are defined as:
∑
We next formulate a game with the Layered DC-net. At
phase 2 of the Layered DC-net, each teacher knows whether
or not. If there is no bullying in any class (i.e.,
), the game among teachers is a com-
plete-information game , where .
Since this game is not relevant to the discussion in this paper,
we do not explain this game here. If there is bullying in a class
(i.e., ), the game among teachers is formulated as a
Bayesian game , where
is the probability distribution of under
the condition that there is bullying in at least one class. The
Bayesian game is transformed to a complete-information
game denoted by , where is defined
as:
∑
V. EVALUATION
In this section, we analyze the game among bystanders and
the game among teachers based on the models described in Sec.
IV in order to evaluate the effectiveness of the Layered DC-net.
A. Evaluation of Game among Bystanders
We first evaluate the effectiveness of the Layered DC-net in a
lower group. In particular, we evaluate the games among by-
standers with and without the Layered DC-net by comparing
the numbers of reports in both games.
In the evaluation, similar to [5], we assume that the game or
is repeatedly played by the following three types of by-
standers. A repetition of a game is called a round.
 Expected Payoff Maximizing Bystander (EPMB)
 Round 1: She randomly plays strategy R or S, each with
probability .
 Round 2 and subsequent rounds: She takes the ratio of
the number of bystanders who played strategy R at the
previous round as an estimated probability q according
to which the other bystanders will play strategy R at the
current round. Based on this q, she compares E �
with ES � where E � and ES � are expected pay-
offs when playing strategies R and S, respectively. If
E � ES � , she plays strategy R with the proba-
bility � + �, else if E � ES � , she plays strategy
R with the probability � �.
 Random Bystander (RB)
In each round, she randomly plays strategy R or S, each
with probability .
 Faithful Bystander (FB
She always plays strategy R in each round.
Unless otherwise specified, the parameters used in this nu-
merical analysis are the same as those in experiment 1 of [5] as
shown in Tab. 2.
Table 2. The parameter configuration
# of bystanders 20
# of three types of
bystanders
EPMB:RB:FB 15:1:4
Threshold 15
Base line 120
Parameter � 0.05
We first investigate the number of reports when
⁄ (i.e., cost is smaller than cost
). Figure 2 shows the expected payoffs for EPMB as func-
tions of � , the probability estimated by EPMB that the
others play strategy R at round . The lines show the expected
payoff E (� ) when playing strategy R without the Layered
DC-net, the expected payoff ES(� ) when playing strategy S
with or without the Layered DC-net and the expected payoff
E (� ) (Anonym) when playing strategy R with the Layered
DC-net.
40

5. Figure 2: Expected Payoffs for bystander at �
( )
In Fig. 2, the expected payoff E (� ) is smaller than the
expected payoff ES(� ) when � 0.58. This indicates
that although there is bullying in the class, bystander is afraid
of retaliation and is likely not to report the bullying when
� 0.58. Meanwhile, the expected payoff with the Layered
DC-net E (� ) (Anonym) is always larger than the expected
payoff ES(� ). In the case that cost is smaller than cost
(i.e., ⁄ ), the Layered DC-net only slightly increases
the expected payoff when reporting bullying.
Figure 3 shows the evolution of the number of reports. In Fig.
3, the average number of reports and the 95% confidence in-
tervals of 100 measurements are plotted. This figure demon-
strates that the number of reports with the Layered DC-net
converges to that without the Layered DC-net as the round
advances.
Figure 3: Evolution of the number of reports
( )
We next investigate the number of reports for
⁄
⁄ (i.e., cost is larger than cost ).
The expected payoff for EPMB as a function of � is shown
in Fig. 4. Figure 4 shows the expected payoffs for EPMB as
functions of � , the probability estimated by EPMB that the
others play strategy R at round . The lines show the expected
payoff E (� ) when playing strategy R without the Layered
DC-net, the expected payoff ES(� ) when playing strategy S
with or without the Layered DC-net and the expected payoff
E (� ) (Anonym) when playing strategy R with the Layered
DC-net.
Fig. 4: Expected Payoffs of bystander at �
( )
In Fig. 4, the expected payoff E (� ) compared with
ES(� ) significantly decreases when � 0.85. Mean-
while, the expected payoff with the Layered DC-net E (� )
(Anonym) does not decrease significantly compared with
E (� ).
Figure 5 shows the evolution of the number of reports. Sim-
ilar to Fig. 3, the average number of reports and the 95% con-
fidence intervals of 100 measurements are plotted in Fig. 5. In
Fig. 5, the number of reports with the Layered DC-net increases
compared with that without the Layered DC-net. By using the
Layered DC-net, the number of reports reaches the threshold
15 at round 2. Meanwhile, the number of reports without
the Layered DC-net does not reach the threshold 15. From
these observations, we conclude that the Layered DC-net is an
effective way to increase the number of reports while main-
taining the anonymity of individuals, in particular, in the case
where cost is larger than cost .
Figure 5: Evolution of the number of reports
( )
B. Evaluation of Game among Teachers
We next evaluate the effectiveness of the Layered DC-net in
the upper group. In particular, we compare the Nash equilibria
of game among teachers with the Layered DC-net to those
of game without the Layered DC-net. The parameter con-
figuration is . The distri-
bution of type, in other words, the existence of bullying in each
class, is given by the following equation.
41

6. {
Table 3 and 4 show the payoffs in game and respec-
tively.
Table 3: Payoffs in game without the Layered DC-net
→
→
→
→
→
→
→
→
→
→
-1.03,
-1.03
-1.03,
-1.03
-1.03,
-1.12
-1.03,
-1.12
→
→
-1.03,
-1.03
-0.09,
-0.09
-1.04,
-1.02
-0.10,
-0.08
→
→
-1.12,
-1.03
-1.02,
-1.04
-1.12,
-1.12
-1.02,
-1.13
→
→
-1.12,
-1.03
-0.08,
-0.10
-1.13,
-1.02
-0.09,
-0.09
Table 4: Payoffs in game with the Layered DC-net
→
→
→
→
→
→
→
→
→
→
-1.55,
-1.55
-1.55,
-1.55
-1.55,
-3.18
-1.55,
-3.18
→
→
-1.55,
-1.55
-1.55,
-1.55
-1.78,
-1.59
-1.78,
-1.59
→
→
-3.18,
-1.55
-1.59,
-1.78
-2.86,
-2.86
-1.27,
-3.09
→
→
-3.18,
-1.55
-1.59,
-1.78
-3.09,
-1.27
-1.50,
-1.50
In Tab. 3, the row where the teacher 1’s strategy
→ → means that teacher 1 agrees to take
school-wide anti-bullying measures irrespective of the exist-
ence of bullying. In this case, when the teacher 2’s strategy
→ → , the payoffs for teachers 1 and 2 are both
-1.03.
In game without the Layered DC-net, the shaded areas of
Tab. 3 (i.e., ( → → → → )
( → → → → ) ( → → →
→ )) are the Nash equilibria. In particular, in the Nash
equilibrium of the bottom right area of Tab.3 (i.e.,
( → → → → )), there is no agreement to
take school-wide anti-bullying measures irrespective of the
existence of bullying in her class. Thus, if there is bullying, the
bullying continues. This implies that when the Layered DC-net
is not used, the bullying might continue.
In the game with the Layered DC-net , the shaded areas
of Tab. 4 (i.e., ( → → → → )
( → → → → ) ( → → →
→ ) ( → → → → )) are the Nash
equilibria. By broadcasting the existence of bullying to teachers
with the Layered DC-net, the set of strategies ( → →
→ → ) that is the undesired Nash equilibrium in
Tab.3 is not a Nash equilibrium in Tab. 4. In the Nash equilibria
in Tab. 4, when there is bullying, school-wide anti-bullying
measures are taken. From these observations, we conclude that
the Layered DC-net implements the Nash equilibria that en-
courage the settling of bullying.
VI. CONCLUSION
In this paper, we have proposed an application of DC-net
called Layered DC-net for encouraging the reporting of
wrongdoing in social groups, structured into layered subgroups
(i.e., lower groups and an upper group). When individuals in
each lower group report wrongdoing, the Layered DC-net can
(1) broadcast the number of reports within each lower group
while maintaining the anonymity of the individuals reporting it
and (2) broadcast the existence of individuals reporting it
within the upper group while maintaining the anonymity of the
individuals reporting it and that of their representative. We
have focused on reporting bullying in a school as an example of
reporting wrongdoing in social groups. By using game theory,
we have formulated a game among bystanders of bullying in a
lower group and another game among teachers in the upper
group. We have evaluated the games with and without the
Layered DC-net. We have concluded that the Layered DC-net
implements the Nash equilibria that encourage the reporting of
wrongdoing in both lower and upper groups and settles
wrongdoing in the social group.
As future works, more investigation is needed on the effec-
tiveness of reporting bullying in schools using the Layered
DC-net. In particular, since the games of the lower groups and
the game of the upper group are related, we need to formulate
games among bystanders and another game among teachers as
a multi-level game [6] and evaluate the multi-level game with
and without the Layered DC-net. Moreover, it is important to
evaluate the Layered DC-net in other social groups other than
the bullying scenario in schools.
REFERENCES
[1] D. Fudenberg and J. Tirole, “Game theory,” MIT press, Cambridge,
Massachusetts, 1991.
[2] D. Chaum, “The dining cryptographers problem,” Journal of Cryptology，
vol. 1，no. 1, pp.65-75, 1988.
[3] E.G. Sirer, S. Goel, M. Robson, and D. Engin, “Eluding Carnivores: File
sharing with strong anonymity,” in Proceedings of the 11th ACM
SIGOPS European Workshop，Feb. 2004.
[4] J. O. Oberender and H. de Meer, “On the design dilemma in dining
cryptographer networks," in proceedings of the 5th International Con-
ference on Trust, Privacy, and Security in Digital Business (TrustBus),
pp. 163-172, Sep. 2008.
[5] A. Shibata, T. Mori, M. Okamura, and N. Soyama, “An economic anal-
ysis of apathetic behavior: Theory and experiment,” Journal of So-
cio-Economics, vol. 37, issue 1, pp. 90-107, Feb. 2008.
[6] K. Hausken, and R. Cressman, “Formalization of multi-level games,”
International Game Theory Review, vol. 6, no. 2, pp. 195-222, 2004.
42